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Tble of Content. Introduction.. Types of friction. 3. Grph of friction. 4. riction is cuse of otion. 5. dvntges nd disdvntges of friction. 6. Methods of chnging friction. 7. ngle of friction. 8. esultnt force exerted by surfce on block. 9. ngle of repose. 0. Clcultion of necessry force in different conditions.. ccelertion of block ginst friction.. Work done ginst friction. 3. Motion of two bodies one resting on the other. 4. Motion of n insect in the rough bowl. 5. Miniu ss hung fro the string to just strt the otion. 6. Mxiu length of hung chin. 7. Coefficient of friction between body nd wedge. 8. topping of block due to friction. 9. topping of two blocks due to friction.
0. Velocity t the botto of rough wedge.. ticking of block with ccelerted crt.. ticking of person fro the wll of rotor.. Introduction. If we slide or try to slide body over surfce the otion is resisted by bonding between the body nd the surfce. This resistnce is represented by single force nd is clled friction. The force of friction is prllel to the surfce nd opposite to the direction of intended otion.. Types of riction. () ttic friction: The opposing force tht coes into ply when one body tends to ove over the surfce of nother, but the ctul otion hs yet not strted is clled sttic friction. (i) If pplied force is nd the body reins t rest then sttic friction =. (ii) If body is t rest nd no pulling force is cting on it, force of friction on it is g zero. (iii) ttic friction is self-djusting force becuse it chnges itself in ccordnce with the pplied force. () Liiting friction: If the pplied force is incresed the force of sttic friction lso increses. If the pplied force exceeds certin (xiu) vlue, the body strts oving. This xiu vlue of sttic friction up to which body does not ove is clled liiting friction. (i) The gnitude of liiting friction between ny two bodies in contct is directly proportionl to the norl rection between the. l Or l s (ii) Direction of the force of liiting friction is lwys opposite to the direction in which one body is t the verge of oving over the other (iii) Coefficient of sttic friction: () s is clled coefficient of sttic friction nd defined s the rtio of force of liiting friction nd norl rection s
(b) Diension: [ M L T ] (c) Unit: It hs no unit. 0 (d) Vlue of s lies in between 0 nd 0 0 (e) Vlue of depends on teril nd nture of surfces in contct tht ens whether dry or wet ; rough or sooth polished or non-polished. (f) Vlue of does not depend upon pprent re of contct. (3) Kinetic or dynic friction: If the pplied force is incresed further nd sets the body in otion, the friction opposing the otion is clled kinetic friction. (i) Kinetic friction depends upon the norl rection. k or where k is clled the coefficient of kinetic friction k (ii) Vlue of k depends upon the nture of surfce in contct. (iii) Kinetic friction is lwys lesser thn liiting friction k k l k s i.e. coefficient of kinetic friction is lwys less thn coefficient of sttic friction. Thus we require ore force to strt otion thn to intin it ginst friction. This is becuse once the otion strts ctully; inerti of rest hs been overcoe. lso when otion hs ctully strted, irregulrities of one surfce hve little tie to get locked gin into the irregulrities of the other surfce. (iv) Types of kinetic friction () liding friction: The opposing force tht coes into ply when one body is ctully sliding over the surfce of the other body is clled sliding friction. e.g. flt block is oving over horizontl tble. (b) olling friction: When objects such s wheel (disc or ring), sphere or cylinder rolls over surfce, the force of friction coes into ply is clled rolling friction. olling friction is directly proportionl to the norl rection () nd inversely proportionl to the rdius (r) of the rolling cylinder or wheel. rolling r r r Is clled coefficient of rolling friction. It would hve the diensions of length nd would be esured in eter.. olling friction is often quite sll s copred to the sliding friction. Tht is why hevy lods re trnsported by plcing the on crts with wheels. b. In rolling the surfces t contct do not rub ech other. 3
orce of friction c. The velocity of point of contct with respect to the surfce reins zero ll the ties lthough the center of the wheel oves forwrd. 3. Grph between pplied orce nd orce of riction. () rt O of the curve represents sttic friction ( s ). Its vlue increses linerly with the pplied force () t point the sttic friction is xiu. This represent liiting friction ( l ). C (3) eyond, the force of friction is seen to decrese slightly. The s portion C of the curve therefore represents the kinetic friction ( k ). l k (4) s the portion C of the curve is prllel to x-xis therefore kinetic friction does not chnge with the pplied force, it reins constnt, nd whtever be the pplied force. O pplied force 4. riction is Cuse of Motion. It is generl isconception tht friction lwys opposes the otion. No doubt friction opposes the otion of oving body but in ny cses it is lso the cuse of otion. or exple : () In oving, person or vehicle pushes the ground bckwrds (ction) nd the rough surfce of ground rects nd exerts forwrd force due to friction which cuses the otion. If there hd been no friction there will be slipping nd no otion. ction riction () In cycling, the rer wheel oves by the force counicted to it by pedling while front wheel oves by itself. o, when pedling bicycle, the force exerted by rer wheel on ground kes force of friction ct on it in the forwrd direction (like wlking). ront wheel oving by itself experience force of friction in bckwrd direction (like rolling of bll). [However, if pedling is stopped both wheels ove by theselves nd so experience force of friction in bckwrd direction.] While pedlling edlling is stoped 4
(3) If body is plced in vehicle which is ccelerting, the force of friction is the cuse of otion of the body long with the vehicle (i.e., the body will rein t rest in the ccelerting vehicle until s g). If there hd been no friction between body nd vehicle the body will not ove long with the vehicle. sg ro these exples it is cler tht without friction otion cnnot be strted, stopped or trnsferred fro one body to the other. 5. dvntges nd Disdvntges of riction. () dvntges of friction (i) Wlking is possible due to friction. (ii) Two body sticks together due to friction. (iii) rke works on the bsis of friction. (iv) Writing is not possible without friction. (v) The trnsfer of otion fro one prt of chine to other prt through belts is possible by friction. () Disdvntges of friction (i) riction lwys opposes the reltive otion between ny two bodies in contct. Therefore extr energy hs to be spent in overcoing friction. This reduces the efficiency of chine. (ii) riction cuses wer nd ter of the prts of chinery in contct. Thus their lifetie reduces. (iii) rictionl force result in the production of het, which cuses dge to the chinery. 5
6. Methods of Chnging riction. We cn reduce friction () y polishing. () y lubriction. (3) y proper selection of teril. (4) y strelining the shpe of the body. (5) y using bll bering. lso we cn increse friction by throwing soe snd on slippery ground. In the nufcturing of tyres, synthetic rubber is preferred becuse its coefficient of friction with the rod is lrger. 7. ngle of riction. ngle of friction y be defined s the ngle which the resultnt of liiting friction nd norl rection kes with the norl rection. y definition ngle is clled the ngle of friction tn tn = [s we know ] or tn ( ) Hence coefficient of liiting friction is equl to tngent of the ngle of friction. g 8. esultnt orce Exerted by urfce on lock. In the bove figure resultnt force ( g) ( g) g When there is no friction ( 0) will be iniu i.e., = g Hence the rnge of cn be given by, g g 6
9. ngle of epose. ngle of repose is defined s the ngle of the inclined plne with horizontl such tht body plced on it is just begins to slide. y definition is clled the ngle of repose. In liiting condition nd o gsin gcos tn tn tn [s we know tn ] Thus the coefficient of liiting friction is equl to the tngent of ngle of repose. s well s i.e. ngle of repose = ngle of friction. g sin g g cos 0. Clcultion of Necessry orce in Different Conditions. If W = weight of the body, = ngle of friction, tn coefficient of friction then we cn clculte necessry force for different condition in the following nner : () Miniu pulling force t n ngle fro the horizontl y resolving in horizontl nd verticl direction (s shown in figure) or the condition of equilibriu cos nd W sin y substituting these vlue in cos ( W sin ) sin cos ( W sin ) [s tn ] cos sin W cos( ) sin W cos 7
() Miniu pushing force t n ngle fro the horizontl y esolving in horizontl nd verticl direction (s shown in the figure) or the condition of equilibriu cos nd W sin y substituting these vlue in cos ( W sin ) sin cos ( W sin ) [s tn ] cos cos W sin cos( ) sin W (3) Miniu pulling force to ove the body up n inclined plne y esolving in the direction of the plne nd perpendiculr to the plne (s shown in the figure) or the condition of equilibriu sin W cos W cos sin nd W sin cos cos W sin y substituting these vlues in nd solving we get + sin cos + W sin W cos sin ( ) W cos( ) (4) Miniu force on body in downwrd direction long the surfce of inclined plne to strt its otion y esolving in the direction of the plne nd perpendiculr to the plne (s shown in the figure 8
or the condition of equilibriu sin W cos W cos sin nd cos W sin y substituting these vlues in nd solving we get cos + + sin W cos W sin( ) W cos( ) (5) Miniu force to void sliding body down n inclined plne y esolving in the direction of the plne nd perpendiculr to the plne (s shown in the figure) or the condition of equilibriu sin W cos W cos sin nd cos W sin W sin cos y substituting these vlues in nd solving we get sin ( ) W cos( ) + sin W sin + cos W cos W (6) Miniu force for otion nd its direction Let the force be pplied t n ngle with the horizontl. y resolving in horizontl nd verticl direction (s shown in figure) or verticl equilibriu sin g g sin.(i) nd for horizontl otion cos i.e. cos.(ii) ubstituting vlue of fro (i) in (ii) cos ( g sin ) + sin cos g 9
g.(iii) cos sin or the force to be iniu (cos sin ) ust be xiu i.e. d [cos sin ] 0 d tn or tn ( ) ngle of friction sin cos 0 i.e. or iniu vlue of its ngle fro the horizontl should be equl to ngle of friction s tn so fro the figure sin nd cos y substituting these vlue in eqution (iii) g g in g. ccelertion of lock ginst riction. () ccelertion of block on horizontl surfce When body is oving under ppliction of force, then kinetic friction opposes its otion. Let is the net ccelertion of the body ro the figure k k k g () ccelertion of block down rough inclined plne When ngle of inclined plne is ore thn ngle of repose, the body plced on the inclined plne slides down with n ccelertion. ro the figure g sin g sin gsin g cos g sin g g cos 0
ccelertion g[sin cos] Note: or frictionless inclined plne 0 g sin. (3) etrdtion of block up rough inclined plne When ngle of inclined plne is less thn ngle of repose, then for the upwrd otion g sin g sin g cos etrdtion g[sin cos] Note: or frictionless inclined plne 0 g sin g sin + g g cos. Work Done ginst riction. () Work done over rough inclined surfce If body of ss is oved up on rough inclined plne through distnce s, then Work done = force distnce = s = g [sin + cos ]s g s[sin cos ] g sin + g s g cos () Work done over horizontl surfce In the bove expression if we put = 0 then Work done = force distnce = s = g s It is cler tht work done depends upon g s (i) Weight of the body. (ii) Mteril nd nture of surfce in contct. (iii) Distnce oved.
3. Motion of Two odies One esting on the Other. When body of ss is resting on body of ss M then two conditions re possible () force is pplied to the upper body, () force is pplied to the lower body We will discuss bove two cses one by one in the following nner: () force is pplied to the upper body, then following four situtions re possible (i) When there is no friction () The body will ove on body with ccelertion (/). / (b) The body will rein t rest 0 (c) If L is the length of s shown in figure will fll fro fter tie t L L t s s t nd / M L (ii) If friction is present between nd only nd pplied force is less thn liiting friction ( < l) ( = pplied force on the upper body, l = liiting friction between nd, k = Kinetic friction between nd ) () The body will not slide on body till i.e. g (b) Cobined syste ( + M) will ove together with coon ccelertion l s M (iii) If friction is present between nd only nd pplied force is greter thn liiting friction ( > l) In this condition the two bodies will ove in the se direction (i.e. of pplied force) but with different ccelertion. Here force of kinetic friction otion of. k g will oppose the otion of while will cuse the k ree body digr k M ree body digr i.e. k ( kg ) k of i.e. kg M k M of M
Note: s both the bodies re oving in the se direction. ccelertion of body reltive to will be L o, will fll fro fter tie t ML M g( M) k M kg( M) M (iv) If there is friction between nd floor (where l ( M ) g = liiting friction between nd floor, k = kinetic friction between nd ) will ove only if k l nd then k l M M However if does not ove then sttic friction will work (not liiting friction) between body nd the floor i.e. friction force = pplied force (= k) not l. l K () force is pplied to the lower body, then following four situtions re possible (i) When there is no friction () will ove with ccelertion (/M) while will rein t rest (reltive to ground) s there is no pulling force on. nd 0 M L M (b) s reltive to, will ove bckwrds with ccelertion (/M) nd so will fll fro it in tie t. t L ML (ii) If friction is present between nd only nd < l (where = seudo force on body nd l = liiting friction between body nd ) () oth the body will ove together with coon ccelertion (b) seudo force on the body, nd l sg M (c) l s g M s ( M) g o both bodies will ove together with ccelertion M if s [ M] g M 3
(iii) If friction is present between nd only nd > l (where l = s ( + M)g = liiting friction between body nd surfce) oth the body will ove with different ccelertion. Here force of kinetic friction k g will oppose the otion of while will cuse the otion of. k g ree body digr k M ree body digr i.e. g k of k i.e. [ kg ] M K of M Note: s both the bodies re oving in the se direction ccelertion of body reltive to will be k g( M) M Negtive sign iplies tht reltive to, will ove bckwrds nd will fll it fter tie t L ML g( M) k (iv) If there is friction between nd floor: The syste will ove only if l. The entire cse (iii) will be vlid. ' l then replcing by However if the syste will not ove nd friction between nd floor will be while between nd is zero. l 4
4. Motion of n Insect in the ough owl. The insect crwl up the bowl up to certin height h only till the coponent of its weight long the bowl is blnced by liiting frictionl force. Let = ss of the insect, r = rdius of the bowl, = coefficient of friction for liiting condition t point Dividing (ii) by (i) gcos...(i) nd l gsin...(ii) tn l s l l r O y r y y or y r g cos g g sin h o h r y r, h r 5. Miniu Mss Hung ro the tring to Just trt the Motion. () When ss plced on rough horizontl plne: nother ss hung fro the string connected by pulley, the tension (T) produced in string will try to strt the otion of ss. t liiting condition T l T g g g g T This is the iniu vlue of to strt the otion. Note: In the bove condition Coefficient of friction () When ss plced on rough inclined plne: nother ss hung fro the string connected by pulley, the tension (T) produced in string will try to strt the otion of ss. 5
t liiting condition or or T g... (i) T g sin T g sin T T T g sin g cos...(ii) ro eqution (i) nd (ii) [sin cos] this is the iniu vlue of to strt the otion g sin + g cos g g Note: In the bove condition Coefficient of friction tn cos 6. Mxiu Length of Hung Chin. unifor chin of length l is plced on the tble in such nner tht its l ' prt is hnging over the edge of tble without sliding. ince the chin hve unifor liner density therefore the rtio of ss or rtio of length for ny prt of the chin will be equl. ss hnging fro the tble We know [ro rticle 5.5] ss lying on the tble or this expression we cn rewrite bove expression in the following nner length hnging fro the tble [s chin hve unifor liner density] length lying on the tble l l l l by solving l ( ) ( l l ) l 6
7. Coefficient of riction between ody nd Wedge. body slides on sooth wedge of ngle nd its tie of descent is t. ooth wedge ough wedge If the se wedge de rough then tie tken by it to coe down becoes n ties ore (i.e. nt) The length of pth in both the cses re se. or sooth wedge u t t ( g sin ) t...(i) ro eqution (i) nd (ii) [ su 0 nd g sin ] ( g sin ) t = sin (sin cos) n g (sin cos)( nt) tn n or rough wedge u t t g(sin cos)( nt)...(ii) [ su 0 nd g(sin cos)] 8. topping of lock Due to riction. () On horizontl rod (i) Distnce trvelled before coing to rest: block of ss is oving initilly with velocity u on rough surfce nd due to friction it coes to rest fter covering distnce. etrding force g g. v = 0 u ro v u 0 u g [s v 0, g] u g 7
or [s oentu = u] g (ii) Tie tken to coe to rest ro eqution v u t 0 u g t [ sv 0, g] t u g (iii) orce of friction cting on the body We know, o, = ( v u) t u [s v = 0] t u g s t g () On inclined rod : When block strts with velocity u its kinetic energy will be converted into potentil energy nd soe prt of it goes ginst friction nd fter trvelling distnce it coes to rest i.e. v = 0. nd we know tht retrdtion g[sin cos] y substituting the vlue of v nd in the following eqution v u v = 0 u 0 u g[sin cos] u g (sin cos) 8
9. topping of Two locks Due to riction. When two sses copressed towrds ech other nd suddenly relesed then energy cquired by ech block will be dissipted ginst friction nd finlly block coes to rest i.e., = E [Where = riction, = Distnce covered by block, E = Initil kinetic energy of the block] [Where = oentu of block] g [s = g] g In given condition nd re se for both the blocks. o 0. Velocity t the otto of ough Wedge. body of ss which is plced t the top of the wedge (of height h) strts oving downwrd on rough inclined plne. Loss of energy due to friction = L (Work ginst friction) E t point = gh KE t point = v y the lw of conservtion of energy i.e. v gh L v L u = 0 h v ( gh L) 9
. ticking of lock with ccelerted Crt. When crt oves with soe ccelertion towrd right then pseudo force () cts on block towrd left. This force () is ction force by block on crt. Now block will rein sttic w.r.t. block. If friction force g [ s ] in g g g This is the iniu ccelertion of the crt so tht block does not fll. nd the iniu force to hold the block together in M ) ( ( M ) in g in g M CT. ticking of erson with the Wll of otor. person with ss stnds in contct ginst the wll of cylindricl dru (rotor). The coefficient of friction between the wll nd the clothing is. If otor strts rotting bout its xis, then person thrown wy fro the center due to centrifugl force t prticulr speed w, the person stuck to the wll even the floor is reoved, becuse friction force blnces its weight in this condition. ro the figure. riction force () = weight of person (g) = g c g [Here, c= centrifugl force] in r g g C in g r 0